EART160 Planetary Sciences

1
EART160 Planetary Sciences
Francis Nimmo
2
Last Week

• Planetary mass and radius give us bulk density
• Bulk density depends on both composition and size
  
• Larger planets have greater bulk densities
  because materials get denser at high pressures
• The increase in density of a material is
  controlled by its bulk modulus
• Planets start out hot (due to accretion) and cool
• Cooling is accomplished (usually) by either
  conduction or convection
• Vigour of convection is controlled by the
  Rayleigh number, and increases as viscosity
  decreases
• Viscosity is temperature-dependent, so planetary
  temperatures tend to be self-regulating

3
Talk tomorrow

• 4pm in NS101
• Matija Cuk, The lunar cataclysm

4
This Week - Atmospheres

• What determines the surface temperature of a
  planet?
• What determines the temperature and pressure
  structure of planetary atmospheres?
• What are the atmospheres made of, and where do
  they come from?
• What determines the wind strengths?
• How do planetary atmospheres evolve?

5
Surface Temperature (1)

• What determines a planets surface temperature?

Reflected energy
Incident energy
Energy re-radiated from warm surface
R
Sun
Absorbed energy warms surface
A is albedo, FE is solar flux at Earths surface,
rE is distance of Earth to Sun, r is distance of
planet to Sun, e is emissivity, s is Stefans
constant (5.67x10-8 Wm-2K-4)

• Balancing energy in and energy out gives

6
Surface Temperature (2)

• Solar constant FE1300 Wm-2
• Earth (Bond) albedo A0.29, e0.9
• Equilibrium temperature 263 K
• How reasonable is this value?

s is Stefans constant 5.67x10-8 in SI units

• How to explain the discrepancies?
• Has the Suns energy stayed constant with time?

7
Greenhouse effect

• Atmosphere is more or less transparent to
  radiation (photons) depending on wavelength
  opacity
• Opacity is low at visible wavelengths, high at
  infra-red wavelengths due to absorbers like water
  vapour, CO2
• Incoming light (visible) passes through
  atmosphere with little absorption
• Outgoing light is infra-red (surface temperature
  is lower) and is absorbed by atmosphere
• So atmosphere heats up
• Venus suffered from a runaway greenhouse effect
  surface temperature got so high that carbonates
  in the crust dissociated to CO2 . . .

8
Albedo effects

• Fraction of energy reflected (not absorbed) by
  surface is given by the albedo A (0ltAlt1)
• Coal dust has a low albedo, ice a high one
• The albedo can have an important effect on
  surface temperature
• E.g. ice caps grow, albedo increases, more heat
  is reflected, surface temperature drops, ice caps
  grow further . . . runaway effect!
• This mechanism is thought to have led to the
  Proterozoic Snowball Earth
• How did the Snowball disappear?
• How did life survive?
• How might clouds affect planetary albedo?

9
Atmospheric Structure (1)

• Atmosphere is hydrostatic
• Gas law gives us
• Combining these two (and neglecting latent heat)

Here R is the gas constant, m is the mass of one
mole, and RT/gm is the scale height of the
(isothermal) atmosphere (10 km) which tells you
how rapidly pressure increases with depth

• Result is that pressure decreases exponentially
  as a function of height (if the temperature stays
  constant)

10
Scale Heights

• The scale height tells you how far upwards the
  atmosphere extends
• Scale height H RT/gm. Does this make physical
  sense?
• Total column mass (per unit area) r0HP0/g
  (wheres this from?)
• It turns out that most planets have similar scale
  heights

Temperature measured at 1bar pressure
11
Atmospheric Structure (2)

• Of course, temperature actually does vary with
  height
• If a packet of gas rises rapidly (adiabatic),
  then it will expand and, as a result, cool
• Work done in expanding work done in cooling

Cp is the specific heat capacity of the gas at
constant pressure
m is the mass of one mole, r is the density of
the gas

• Combining these two equations with hydrostatic
  equilibrium, we get the dry adiabatic lapse rate

• On Earth, the lapse rate is about 10 K/km
• What happens if the air is wet?

12
Atmospheric Structure (3)

• Lower atmosphere (opaque) is dominantly heated
  from below and will be conductive or convective
  (adiabatic)
• Upper atmosphere intercepts solar radiation and
  re-radiates it
• There will be a temperature minimum where
  radiative cooling is most efficient (the
  tropopause)

radiation
Temperature (schematic)
mesosphere
stratosphere
tropopause
Lapse rate appx. 1.6 K/km why?
clouds
troposphere
adiabat
Measured Martian temperature profiles
13
Giant planet atmospheric structure

• Note position and order of cloud decks

14
Atmospheric dynamics

• Coriolis effect objects moving on a rotating
  planet get deflected (e.g. cyclones)
• Why? Angular momentum as an object moves
  further away from the pole, r increases, so to
  conserve angular momentum w decreases (it moves
  backwards relative to the rotation rate)
• Coriolis acceleration 2 w v sin(q)
• How important is the Coriolis effect?

Deflection to right in N hemisphere
q is latitude
is a measure of its importance (Rossby number)
e.g. Jupiter v100 m/s, L10,000km we get 30 so
important
15
Hadley Cells

• Coriolis effect is complicated by fact that
  parcels of atmosphere rise and fall due to
  buoyancy (equator is hotter than the poles)

High altitude winds
Surface winds

• The result is that the atmosphere is broken up
  into several Hadley cells (see diagram)
• How many cells depends on the Rossby number (i.e.
  rotation rate)

Slow rotator e.g. Venus
Fast rotator e.g. Jupiter
Medium rotator e.g. Earth
Ro0.02 (assumes v100 m/s)
Ro4
Ro30
16
Zonal Winds

• The reason Jupiter, Saturn, Uranus and Neptune
  have bands is because of rapid rotations (periods
  10 hrs)
• The winds in each band can be measured by
  following individual objects (e.g. clouds)
• Winds alternate between prograde (eastwards) and
  retrograde (westwards)

17
Geostrophic balance

• In some situations, the only significant forces
  acting are due to the Coriolis effect and due to
  pressure gradients
• The acceleration due to pressure gradients is
• The Coriolis acceleration is 2 w v sinq (Which
  direction?)
• In steady-state these balance, giving

Why?
L
Does this make sense?
L
wind

• The result is that winds flow along isobars and
  will form cyclones or anti-cyclones
• What are wind speeds on Earth?

pressure
Coriolis
isobars
H
18
Where do planetary atmospheres come from?

• Three primary sources
• Primordial (solar nebula)
• Outgassing (trapped gases)
• Later delivery (mostly comets)
• How can we distinguish these?
• Solar nebula composition well known
• Noble gases are useful because they dont react
• Isotopic ratios are useful because they may
  indicate gas loss or source regions (e.g. D/H)
• 40Ar (40K decay product) is a tracer of
  outgassing

19
Atmospheric Compositions

• Isotopes are useful for inferring outgassing and
  atmos. loss

20
Not primordial!

• Terrestrial planet atmospheres are not primordial
  (How do we know?)
• Why not?
• Gas loss (due to impacts, rock reactions or Jeans
  escape)
• Chemical processing (e.g. photolysis, rock
  reactions)
• Later additions (e.g. comets, asteroids)
• Giant planet atmospheres are close to primordial

Values are by number of molecules
Why is the H/He ratio not constant?
21
Atmospheric Loss

• Atmospheres can lose atoms from stratosphere,
  especially low-mass ones, because they exceed the
  escape velocity (Jeans escape)
• Escape velocity ve (2 g R)1/2 (wheres this
  from?)
• Mean molecular velocity vm (2kT/m)1/2
• Boltzmann distribution negligible numbers of
  atoms with velocities gt 3 x vm
• Molecular hydrogen, 900 K, 3 x vm 11.8 km/s
• Jupiter ve60 km/s, Earth ve11 km/s
• H cannot escape gas giants like Jupiter, but is
  easily lost from lower-mass bodies like Earth or
  Mars
• A consequence of Jeans escape is isotopic
  fractionation heavier isotopes will be
  preferentially enriched

22
Atmospheric Evolution

• Earth atmosphere originally CO2-rich, oxygen-free
• How do we know?
• CO2 was progressively transferred into rocks by
  the Urey reaction (takes place in presence of
  water)

• Rise of oxygen began 2 Gyr ago (photosynthesis
  photodissociation)
• Venus never underwent similar evolution because
  no free water present (greenhouse effect, too
  hot)
• Venus and Earth have same total CO2 abundance
• Urey reaction may have occurred on Mars (water
  present early on), but very little carbonate
  detected

23
Summary

• Surface temperature depends on solar distance,
  albedo, atmosphere (greenhouse effect)
• Scale height and lapse rate are controlled by
  bulk properties of atmosphere (and gravity)
• Terrestrial planetary atmospheres are not
  primordial affected by loss and outgassing
• Coriolis effect organizes circulation into
  cells and is responsible for bands seen on
  giant planets
• Isotopic fractionation is a good signal of
  atmospheric loss due to Jeans escape
• Significant volatile quantities may be present in
  the interiors of terrestrial planets

24
Key Concepts

• Albedo and opacity
• Greenhouse effect
• Snowball Earth
• Scale height
• Lapse rate
• Tropopause
• Coriolis effect
• Hadley cell
• Geostrophic balance
• Jeans escape
• Urey reaction
• Outgassing

H RT/gm
2 w v sin(q)
25
(No Transcript)
26
Thermal tides

• These are winds which can blow from the hot
  (sunlit) to the cold (shadowed) side of a planet

Solar energy added
trotation period, Rplanet radius, rdistance
(AU)
4pR2CpP/g
Atmospheric heat capacity
Wheres this from?
Extrasolar planet (hot Jupiter)
So the temp. change relative to background
temperature
Small for Venus (0.4), large for Mars (38)